Hi Philippe, When stuck with a similar problem, I used EFA-within-CFA (see slides 133-146 of the Mplus short courses handouts 1). In fact, we coined it ESEM-within-CFA in that we followed the methods of EFA-within-CFA and used the specific results from the full ESEM model as starts values for the first order factors (to the degree of fixing the cross loadings that need to be fixed for identification purposes to their ESEM values rather than 0). Then, you simply need to load them on the second order factor (and to ensure they are identified). No sure how to do the reverse: first order CFA model and second order EFA.

Further to the discussion above, I was wondering whether a higher-order ESEM model can be performed in Mplus 6.12?

I am aware of the approach adopted by Marsh, Muthen et al. (2009) published in SEM in which they employed the correlations between the first-order factors as the input for the second-order latent variable.

The first factor loading is fixed to one as the default to set the metric of the factor. I don't know why the third is being fixed to one. Please send the output and your license number to support@statmodel.com.

Sorry for the inconvenience, but I have two questions regarding Model Respecification:

1. My model showed multicollinearity with all 3 Factors. However, as i simple can't do a single or two factor model, i’ve conducted a 2nd Order Factor. As Fit indices are still a bit far from standard cut-offs, i tested a few cross-loadings. The question is: which method should i use? Trust ESEM suggestions from 1st Order Factors and run higher cross-loads or instead trust Mod Indices as i’m already running a 2nd Factor Order Model?

2. In one of my competing models (within 2nd Order Factors) i tested not to fix 1st Order Factors variance to 1. The result was one negative residual factor. From hear, i constrained this factor variance to zero, resulting in far better Fit Indices. Does it make any sense?